$A$ $B$ $C$ If: $ BC = 5x + 6$, $ AC = 125$, and $ AB = 9x + 7$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 7} + {5x + 6} = {125}$ Combine like terms: $ 14x + 13 = {125}$ Subtract $13$ from both sides: $ 14x = 112$ Divide both sides by $14$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $BC$ $ BC = 5({8}) + 6$ Simplify: $ {BC = 40 + 6}$ Simplify to find ${BC}$ : $ {BC = 46}$